Question

The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 3643 miles, with a variance of 196,249. If he is correct, what is the probability that the mean of a sample of 40 cars would be less than 3675 miles? Round your answer to four decimal places.

Answer 1

Given,

= 3643 , = sqrt (196249) = 443

Using central limit theorem,

P( < x) = P (Z < x - / ( / sqrt(n) ) )

So,

P( < 3675) = P( Z < 3675 - 3643 / (443 / sqrt(40) ) )

= P( Z < 0.4569)

= 0.6761 (Probability calculated from Z table)